The sum of several numbers divided by their count nicely summarizes the overall size of the numbers involved in a single value.

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How to add and subtract values from an average?

Say I have 100 numbers that are averaged: number of values = 100 total sum of values = 2000 mean = 2000 / 100 => 20 If I want to add a value and find out the ...
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4answers
177 views

If $\sum\limits_{k=1}^n y_k\geq n$ and $\sum\limits_{k=1}^n \frac{1}{y_k}\geq n$, then $\prod\limits_{k=1}^n y_k\geq 1$?

Let $y_1,\ldots y_n$ be positive real numbers satisfying $y_1+\cdots+y_n\geq n$ and $\displaystyle{\frac{1}{y_1}+\cdots+\frac{1}{y_n}\geq n}$. Is it true that $y_1y_2\cdots y_n\geq 1$?
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3answers
235 views

Erased number?

A set of consecutive positive integers starting with 1 is written on the board. A student came along and erased one number. Average of remaining numbers is 61 15/20 . What was the number erased
3
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3answers
230 views

Definition of random

Suppose that you has to guess given a set of numbers If they are random. The mathematical expectation Is there a definition of randomness that allow this prove/test? Is even possible? if so: How ...
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3answers
56 views

The average value of the function $y=\tan(2x)$ over the interval $[0,\frac{\pi}{8}]$

I was given the following question in a technology free exam. How would one go about solving this without the use of a calculator? NB. I am currently in my last year of high school so please don't ...
3
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2answers
194 views

How to find the average value of $y = e^x$ between $x = e$ and $x = 2e$? [closed]

What approach would be ideal in finding the average value of $y = e^x$ between $x = e$ and $x = 2e$?
3
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2answers
1k views

Average Distance Between Random Points in a Rectangle

My question is similar to this one but for rectangles instead of lines. Suppose I have a rectangle with sides of length $L_w$ and $L_h$. What is the average distance between two uniformly-distributed ...
3
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1answer
48 views

What is the most elementary proof of these inequalities?

Let $p$ be a non-zero integer, and let $x_1$, $\ldots$, $x_n$ be $n$ positive real numbers. Then we define the $p$-th power mean $M_p$ of these numbers as $$ M_p \colon= (\frac{x_1^p + \ldots + ...
3
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1answer
397 views

The Exponential decay.

I am studying semiconductor physics. there is a paragraph about Drude model in E.spenke's book "Electronic semiconductors" page 259 in art §9: "if on the average, a time $τ$ elapses between two ...
3
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1answer
63 views

Is it always true that “max $\ge$ average + sigma”?

Assume that $i$ from $1,\ldots,N$, $x_i \ge 0$ and: $$\mathrm{avg} = \frac{\sum_i x_i}{N}$$ $$\sigma = \sqrt\frac{\sum_i{(x_i-\mathrm{avg})^2}}{N}$$ Is that true that: $$\max_i x_i \ge ...
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2answers
885 views

APR Calculation

I'm hoping someone can clarify this for me. The model/example is this: We lend an amount of 1498.50 (loan amount). Other fees total 39.95. The term of the loan is for 12 months. There is no ...
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2answers
167 views

Expressing a summation using matrix algebra

Consider the $n \times r$ matrix $$\begin{pmatrix} X_{11} & X_{12} & \cdots & X_{1n} \\ X_{21} & X_{22} & \cdots & X_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ ...
3
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1answer
40 views

Is the norm of the average $\le$ the norm of the max?

Given $\pmb X \in \mathcal{R}^p$, denote the elements of $\pmb X$ as $\pmb x_i$ for $i= 1, \dots, n$. Denote the $t(\pmb X)$ as the average of $\pmb X$ \begin{equation} \pmb t(\pmb X) = \frac 1 n ...
3
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1answer
90 views

How do I average a new number into an established percentage if I know the number of items?

This seems like something I should be able to do but I can not for the life of me figure it out. I'm writing a program to calculate an average score; let's say that my data looks like this. x = ...
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2answers
275 views

Course Grade - Statistics Question

I'm confused about finding the standard deviation of various weighted objects in a problem. For example, consider an academic setting, with four assessments as follows: ...
3
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1answer
1k views

leading and lagging moving average indicator

What are leading short and lagging long moving average indicators and how do we calculate them? e.g. for the following data set, and let window size be 2. Can you ...
3
votes
1answer
113 views

How to find the function $f$ that satisfies $f(x, y) = f(x^{-1}, y^{-1})^{-1}$ and $f(x, y)$ is $\approx$ $average(x, y)$?

Fist of all, I'm a programmer, not a mathematician, and I'm sorry for my non native English. And I'm sorry if the question is not appropriate, it is my first time here. Or if the question has no ...
3
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1answer
25 views

Simplified Averages - Always true?

While working on an "average rating" function for a website, I came across an idea for simplified averages, but I want to confirm that it always works. If it does, I might be able to keep a running ...
3
votes
2answers
657 views

What do curly brackets mean in this formula?

In this paper, in the Formula at the beginning of 2.2, we have $B=\{b_i(O_t)\}$ where $i=0,1$ - the number of probability formula $O_t$ - the state at moment $t$ $b_i(O_t)$ - two probabilities ...
3
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1answer
65 views

Mean value of the rotation angle is 126.5°

In the paper "Applications of Quaternions to Computation with Rotations" by Eugene Salamin, 1979 (click here), they get 126.5 degrees as the mean value of the rotation angle of a random rotation (by ...
2
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3answers
98 views

Problem with calculating average.

I came across the following question. A man travels a distance of $20$ miles at $60$ miles/hr and then return over the same route at $40$ miles/hr. What is the average rate for the round trip in ...
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3answers
195 views

Average amount of money received from pulling three random coins

Let's say I have a bag of coins, which contains 1 quarter, 2 dimes, 3 nickles and 4 pennies. If I were to randomly pull out 3 coins, on average, how much money would I get?
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3answers
65 views

What is the mean score for the $20$ rolls?

A fair die is rolled twenty times. The results are shown in the bar graph. What is the mean score for the $20$ rolls?
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3answers
96 views

Average of the smaller of three random numbers from $0$ to $1$

A friend of mine claims he saw the following question on a math puzzle site:- What is the average of the smaller of three random numbers from $0$ to $1$? And they've given these options:- $A) ...
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3answers
433 views

Averaging the values of $\cos x$ over one period

I'm calculating the average value of $\cos x$ by dividing the period $[0,2\pi]$ into ten intervals which means that I should be looking for the average of 11 results. What I get is approx. 0.09. The ...
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3answers
65 views

Why should ${\sum_1^n {s_i} \over \sum_1^n {t_i}} = {n \over \sum_1^n{t_i \over s_i}}$? (harmonic mean)

I realized it reading about computer performance. This identity is presented there with words: dividing total distance by total time, you arrive at average execution rate on the left. On the right, ...
2
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1answer
396 views

Need help with a math trick question

I wasnt sure where to ask this but since this is an algorithmic question here it goes. I've come face to face with a math problem and can't seem to get over it for the last couple of days. It goes ...
2
votes
2answers
25 views

A Percentage of Averages

A company brags about the speed of their service, "75% of our assignments are completed in an average of 20 days." Is this a meaningful claim? Or is it kind of like saying, "60% of the time, it ...
2
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2answers
84 views

Averages in series

I have a series of numbers: $1,2,3$ I'm calculating a simple average between, them $(2)$. Now, I'm deleting the series and have no information regarding how many elements there were in the series or ...
2
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3answers
67 views

Correct way to get average price

probably a basic question for a lot of you guys, but it was a subject of a friendly debate at my work earlier - needless to say none of the involved were accountants. In short, we are thinking about ...
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1answer
60 views

What is this physics simulation formula doing?

I have encountered a piece of code that performs a physics simulation of a moving projectile. I'm trying to understand what the mathematical basis is for a bit that looks like this: $$ d_1 = f(x) $$ ...
2
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1answer
72 views

How to calculate new mean if population is unknown?

I have three values Mean (population mean, not from sample) $\bar{x} = 3$ Number of elements in population (number of values in original set) $n = 15$ A new value $x_{(n+1)} = 7$ What is ...
2
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2answers
123 views

Calculating statistic for multiple runs

I have s imple, general question regarding calculating statistic for N runs of the same experiment. Suppose I would like to calculate mean of values returned by some Test. Each run of the test ...
2
votes
2answers
2k views

Finding percentile rank without knowledge of distribution

Say you take a test and are told your individual score, as a percentage. Eg: 95%. You are also told the aggregate score (average) of all students together, as well as how many students in total took ...
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4answers
617 views

Get `n` random values between 2 numbers having average `x`

I want to get n random numbers(e.g n=16)(whole numbers) between 1 to 5(including both) so that average is x. x can be any value between (1, 1.5, 2, 2.5, 3, 3.5, 4, ...
2
votes
2answers
236 views

Probability cut-off

Is there a probability cut-off point? e.g. if the probability of something keeps halving do you stop at a certain point and say the rest of the possibilities are negligible? What do you do then? ...
2
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1answer
36 views

Average Number of Roots of a Polynomial modulo p

Let $f \in \mathbb{Z}[X]$ be an irreducible non-constant polynomial, and consider this polynomial modulo $p$ for each prime $p$. On average, how many roots does $f$ have modulo $p$? I.e., if $r(p)$ ...
2
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1answer
109 views

Geometric Mean of an Interval

Is there any way to calculate one? If it't not clear what I mean, here's an example: Starting with an initial value, keep multiplying it by some random amount on the interval [1, 2] at regular ...
2
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4answers
446 views

Finding mean of $n$ consecutive numbers using a shortcut

I am working on the following question: Let us say we have $n$ consecutive numbers labelled $x_1$ to $x_n$. I want to find the average of these. The quickest way to do this seems to be ...
2
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2answers
678 views

How do I average out to a particular number if I have to add another number to get that average?

So, lets say, that you have the following numbers (4, 15, 3, 22) and you have to add the fifth number (which I would call X) and they must average out to say 20. What do you have to do? I figured ...
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1answer
171 views

Time to extinction

Suppose that a population has a rate of extinction equal to $k \exp({-\epsilon N})$ where $\epsilon$ and $k$ are constant and $N$ is the population size. This also means that the time to extinction is ...
2
votes
1answer
153 views

Is there a scientific way to assign weights to historical data?

This is a common question I usually face while processing historical data. I have year on year data of an event for the past N years.I would like to assign weights to the data of these N years so that ...
2
votes
1answer
73 views

Estimate the true mean: given only measurements above a known threshold

I have a computer-generated logfile which shows events which took longer than a particular time threshold (say 1 second for the sake of argument): if I measure the mean of these measurements, it seems ...
2
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2answers
252 views

Least Squares Fit

So here's the question: Given a collection of points $(x_1,y_1), (x_2,y_2),\ldots,(x_n,y_n)$, let $x=(x_1,x_2,\ldots,x_n)^T$, $y=(y_1,y_2,\ldots,y_n)^T$, $\bar{x}=\frac{1}{n} ...
2
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1answer
105 views

Is the average of all $x$ such that $0 \le x \le 1$ $ \forall $ $x \in \mathbb{R}$ equal to $\frac{1}{2}$?

Is the average of all $x$ such that $0 \le x \le 1$ $ \forall $ $x \in \mathbb{R}$ equal to $\frac{1}{2}$ ? It may seem this way but how can we show that indeed it is $\frac{1}{2}$. We know that the ...
2
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1answer
116 views

What is the best way to average the frequency of Chinese characters in a sentence?

I'm trying to find the best way to assign a "frequency score" to sentences in Chinese. Basically, I have a database which tells me how frequent each Chinese character is. From that, I would like to ...
2
votes
2answers
189 views

How can I show this in a summation?

I am trying to work out a summation for packet delays which is very similar to the summation for estimating RTT, which is an exponentially weighted moving average. I have modified the estimating RTT ...
2
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1answer
48 views

Average question GRE

The average daily temperature from 9th to 16th January(both inclusive) was 38.6 C and that from the 10th to 17th January(inclusive) was 39.2 C. what was the temperature on 17th January? I am able ...
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1answer
27 views

Problem about average of cos square (nt) where n is arbitrary

I often see people just say time average of cos^2(nwt) is 1/2, I want to know in what cases this is not valid? w is just the frequency, can be assumed as a constant. Assuming you are always ...
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1answer
18 views

Choosing two sets of values with the least difference between the averages of the sets

This is probably a simple Combination problem but I can't think of how to solve it in LibreOffice. I run multiplayer games along with seven of my friends, on two teams of 4 players each, for a total ...